Lattices from Hermitian function fields

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• 作者：Albrecht Bö ; ttcher^a ; ^{aboettch@mathematik.tu-chemnitz.de" class="auth_mail" title="E-mail the corresponding author} ; Lenny Fukshansky^b ; ^{lenny@cmc.edu" class="auth_mail" title="E-mail the corresponding author} ; Stephan Ramon Garcia^c ; ^{stephan.garcia@pomona.edu" class="auth_mail" title="E-mail the corresponding author} ; Hiren Maharaj^b ; ^{hmahara@g.clemson.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11H06 ; secondary ; 11G20
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：447
• 期：Complete
• 页码：560-579
• 全文大小：442 K

文摘

We consider the well-known Rosenbloom–Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of Gerhard Hiss on the factorization of functions with particular divisor support into lines and their inverses.